PSI - Issue 2_A

W. Hu et al. / Procedia Structural Integrity 2 (2016) 066–071 Author name / Structural Integrity Procedia 00 (2016) 000–000

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metal parameter, ΔK. Now, f or a constant ΔG, the value of da/dN should be faster for a higher R-ratio (or load ratio) in the cyclic fatigue test, as the mean stress increases with the increase in the R-ratio. However, Rans, Alderliesten, & Benedictus (2011) questioned the appropriateness of using ΔG to characterize delamination growth in composite structures, as they found that there are test results where a decrease of da/dN occurs with an increasing R-ratio, for a given value of ΔG . In the present paper, Mode I, Mode II and Mixed mode I/II fatigue test data from the literature are analysed. The results of this analysis indicate that ΔG is not a suitable term to be used as a CDF for the delamination in composites under fatigue loadings . Two CDFs other than ΔG are discussed in the paper that are consistent with the corollary. In linear elastic fracture mechanics (LEFM), the stress intensity factor, K, is used to characterize the stress state around the crack tip and is formulated as Eq. (2): = √ 2 ( ) + ⋯ (2) where r is the distance between the point to the crack tip, θ is the angle measured from the extension of the crack line and the higher order terms are ignored. This equation also demonstrates that the stress state at the crack tip is dominated by the r -1/2 singularity. In LEFM, the stress and K are linearly proportional as shown in Eq. (2) and the term ΔK can be expressed as Eq. (3): ∆ = − = (1 − ) (3) where K max and K min are the maximum and minimum stress intensity factor in one fatigue cycle and R is the ratio of the minimum applied load to the maximum applied load in one fatigue cycle. Unlike metals, the stress intensity factor cannot represent the stress state of the delamination growing in the polymeric matrix, or at an interface, between the plies of the fibers. Thus, the SERR is the dominant measurement to evaluate the delamination in LEFM and it has the relationship to the stress intensity factor, K, as shown in Eq. (4): = K 2 (4) where E is the elastic modulus . Hence, Eq. (3) can be re-written with respect to the R-ratio as: ∆ = (1 − 2 ) (5) It is often assumed that the term ΔG can show R-ratio effects in a similar manner to the term ΔK . For a given value of ΔG, an increase in the R-ratio would increase both the maximum and minimum SERR, and hence increase the mean stress. As a consequence, for a given carbon fiber epoxy Toray P305 prepreg of Toray T300/#2500. The double cantilever beam (DCB) specimen geometry consisted of 32 plies of laminates which is 125 mm long and 20 mm wide. The initial delamination length was 20 mm. The resultant da/dN versus ΔG curves associated with R = 0.2, 0.5 and 0.7 are shown in Fig. 1 which reveals that, when plotted in this fashion, the curves of da/dN versus ΔG shift to the right, with increasing R-ratio. This means that for a given value of ΔG, the DCB specimens tested using higher R-ratio values would have slower delamination rates. This is contrary to the metal results (Hartman & Schijve, 1970; Boyce & Ritchie, 2001; Schonbauer, et al., 2014), as well as the expectation associated with a valid CDF. 2. The R-ratio effect and Δ G